Aaronson is just trying to make the point that it's possible to make a formal distinction between nondeterminism and randomness. Mathematically, a nondeterministic function is a function that returns a set of values rather than a value, and a random function is a function that returns a probability distribution over values rather than a value. The fact that we can make such a formal distinction suggests that we ought to also be able to make an informal distinction.